Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)

The main objective of this research is to compute the nonabelian tensor squares of some Bieberbach groups with elementary abelian 2-groups point groups, C2C2 for both abelian and nonabelian cases. This is qualitative research where the computational method for polycyclic groups is used to determine...

Full description

Saved in:

Bibliographic Details
Main Author:	Nor Fadzilah Abdul Ladi
Format:	thesis
Language:	eng
Published:	2018
Subjects:	QA Mathematics
Online Access:	https://ir.upsi.edu.my/detailsg.php?det=3687
Tags:	Add Tag No Tags, Be the first to tag this record!

id	oai:ir.upsi.edu.my:3687
record_format	uketd_dc
spelling	oai:ir.upsi.edu.my:36872020-02-27 Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR) 2018 Nor Fadzilah Abdul Ladi QA Mathematics The main objective of this research is to compute the nonabelian tensor squares of some Bieberbach groups with elementary abelian 2-groups point groups, C2C2 for both abelian and nonabelian cases. This is qualitative research where the computational method for polycyclic groups is used to determine the nonabelian tensor squares of four Bieberbach groups with point group C2 C2. The findings show that the structures of the nonabelian tensor squares of some of these groups for both abelian and nonabelian cases are found split while some are found non-split. The formulas of the abelian cases of the nonabelian tensor squares of the groups lead to the construction of the formulations of the nonabelian tensor squares of arbitrary dimension. Furthermore, for the nonabelian cases, the presentations of the nonabelian tensor squares of the other two groups are given and it was shown that the nonabelian tensor squares can be written as a direct product with the nonabelian exterior square as one of the factor. As a conclusion, the formulas of the nonabelian tensor squares of four Bieberbach groups with point group C2 C2 are developed based on its group presentations of lowest dimension and the formulas of the abelian cases can be generalized up to dimension n. As the implication, this research contributes new theoretical results in the field of theoretical and computational group theory on computing the nonabelian tensor squares of Bieberbach groups with elementary abelian 2-group point group. The results in this research will also benefit to other group theorist who are interested of the computation of the computation of the homological functors. 2018 thesis https://ir.upsi.edu.my/detailsg.php?det=3687 https://ir.upsi.edu.my/detailsg.php?det=3687 text eng closedAccess Masters Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik N/A
institution	Universiti Pendidikan Sultan Idris
collection	UPSI Digital Repository
language	eng
topic	QA Mathematics
spellingShingle	QA Mathematics Nor Fadzilah Abdul Ladi Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)
description	The main objective of this research is to compute the nonabelian tensor squares of some Bieberbach groups with elementary abelian 2-groups point groups, C2C2 for both abelian and nonabelian cases. This is qualitative research where the computational method for polycyclic groups is used to determine the nonabelian tensor squares of four Bieberbach groups with point group C2 C2. The findings show that the structures of the nonabelian tensor squares of some of these groups for both abelian and nonabelian cases are found split while some are found non-split. The formulas of the abelian cases of the nonabelian tensor squares of the groups lead to the construction of the formulations of the nonabelian tensor squares of arbitrary dimension. Furthermore, for the nonabelian cases, the presentations of the nonabelian tensor squares of the other two groups are given and it was shown that the nonabelian tensor squares can be written as a direct product with the nonabelian exterior square as one of the factor. As a conclusion, the formulas of the nonabelian tensor squares of four Bieberbach groups with point group C2 C2 are developed based on its group presentations of lowest dimension and the formulas of the abelian cases can be generalized up to dimension n. As the implication, this research contributes new theoretical results in the field of theoretical and computational group theory on computing the nonabelian tensor squares of Bieberbach groups with elementary abelian 2-group point group. The results in this research will also benefit to other group theorist who are interested of the computation of the computation of the homological functors.
format	thesis
qualification_name
qualification_level	Master's degree
author	Nor Fadzilah Abdul Ladi
author_facet	Nor Fadzilah Abdul Ladi
author_sort	Nor Fadzilah Abdul Ladi
title	Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)
title_short	Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)
title_full	Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)
title_fullStr	Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)
title_full_unstemmed	Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)
title_sort	formulation of the nonabelian tensor squares of some bieberbach groups with point group c2xc2: abelian and nonabelian cases (ir)
granting_institution	Universiti Pendidikan Sultan Idris
granting_department	Fakulti Sains dan Matematik
publishDate	2018
url	https://ir.upsi.edu.my/detailsg.php?det=3687
_version_	1747833097239396352

Formulation of the nonabelian tensor squares of some bieberbach groups with point group C2XC2: Abelian and nonabelian cases (IR)

Similar Items